Charged Rotating Black Branes in Various Dimensions

TL;DR

This thesis investigates the thermodynamics and stability of charged rotating black branes in various dimensions, deriving formulas, analyzing phase stability, and exploring vortex solutions in four-dimensional cases.

Contribution

It provides new thermodynamic formulas, stability analysis, and vortex solutions for charged rotating black branes, extending understanding in higher-dimensional gravity.

Findings

Thermodynamic potentials are derived in different ensembles.

The system is thermally stable with no Hawking-Page transition.

Vortex solutions exist for Abelian Higgs fields in 4D rotating charged black string background.

Abstract

In this thesis, two different aspects of asymptotically charged rotating black branes in various dimensions are studied. In the first part, the thermodynamics of these spacetimes is investigated, while in the second part the no hair theorem for these spacetimes in four dimensions is considered. In part I, first, the Euclidean actions of a d-dimensional charged rotating black brane are computed through the use of the counterterms renormalization method both in the canonical and the grand-canonical ensemble, and it is shown that the logarithmic divergencies associated to the Weyl anomalies and matter field vanish. Second, a Smarr-type formula for the mass as a function of the entropy, the angular momenta and the electric charge is obtained, which shows that these quantities satisfy the first law of thermodynamics. Third, by using the conserved quantities and the Euclidean actions, the thermodynamics potentials of the system in terms of the temperature, the angular velocities and the electric potential are obtained both in the canonical and the grand-canonical ensemble. Fourth, a stability analysis in these two ensembles is performed, which shows that the system is thermally stable. This is in commensurable with the fact that there is no Hawking-Page phase transition for black object with zero curvature horizon. Finally, the logarithmic correction of the entropy due to the thermal fluctuation around the equilibrium is calculated. In part II, the cosmological defects are studied, and it is shown that the Abelian Higgs field equations in the background of a four-dimensional rotating charged black string have vortex solutions.